Multistable solitons in the cubic-quintic discrete nonlinear Schrödinger equation

R. Carretero-González*, J. D. Talley, C. Chong, B. A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We analyze the existence and stability of localized solutions in the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with a combination of competing self-focusing cubic and defocusing quintic onsite nonlinearities. We produce a stability diagram for different families of soliton solutions that suggests the (co)existence of infinitely many branches of stable localized solutions. Bifurcations that occur with an increase in the coupling constant are studied in a numerical form. A variational approximation is developed for accurate prediction of the most fundamental and next-order solitons, together with their bifurcations. Salient properties of the model, which distinguish it from the well-known cubic DNLS equation, are the existence of two different types of symmetric solitons and stable asymmetric soliton solutions that are found in narrow regions of the parameter space. The asymmetric solutions appear from and disappear back into the symmetric ones via loops of forward and backward pitchfork bifurcations.

Original languageEnglish
Pages (from-to)77-89
Number of pages13
JournalPhysica D: Nonlinear Phenomena
Issue number1 SPEC. ISS.
StatePublished - 1 Apr 2006


FundersFunder number
SDSU Foundation
U.S. Air Force
European Office of Aerospace Research and Development


    • Bifurcations
    • Nonlinear Schrödinger equation
    • Nonlinear lattices
    • Solitons


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